import arrow.Proof

import arrow.TypeProof

interface Semigroup<A> {
  fun A.combine(other: A): A
  interface Syntax<A> {
    val value: A
    fun combine(other: A): A
  }
}

interface Monoid<A> : Semigroup<A> {
  fun empty(): A
}

object StringMonoid : Monoid<String> {
  override fun String.combine(other: String): String = this + other
  override fun empty(): String = ""
}

inline class StringSyntax(override val value: String): Semigroup.Syntax<String> {
  override fun combine(other: String): String = value + other
}

@Proof(TypeProof.Extension)
fun String.Companion.monoid(): Monoid<String> = StringMonoid

@Proof(TypeProof.Extension)
fun String.semigroupSyntax(): Semigroup.Syntax<String> = StringSyntax(this)